Statistical Energy Analysis of Membrane-Type Acoustic Metamaterials in Double Wall Arrangements

Abstract

Acoustic insulation has been a longstanding challenge, persisting into the 21st century despite theoretical advancements, notably in sectors like vehicular refinement. Structural density constraints have posed significant setbacks, driving the emergence of promising solutions such as metamaterials, particularly local resonance metamaterials, which have overcome prior limitations. These advancements have unveiled new possibilities, including membrane-type metamaterials and double-wall arrays, demonstrating encouraging results for acoustic insulation in lightweight structures. Concurrently, recent studies have explored numerical methods and analytical models to understand the behavior of vibroacoustic systems based on metamaterials. Despite promising advancements, further work is needed to develop analysis methods that comprehensively describe the behavior of these emerging noise control systems, particularly within the context of product development. Statistical Energy Analysis (SEA) stands out as a crucial technique in refining vibracoustic requirements and specifications during development schemes, contributing significantly to enhancing the quality, performance, and reliability of the final product. In the realm of metamaterial mechanics, coupling loss factors quantify the efficiency of energy transfer between subsystems. Various methods have been proposed for wave propagation analysis in metamaterials, notably the Plane Wave Expansion (PWE) method and the Transfer Matrix Method (TMM), each presenting advantages and disadvantages with implications for industrial applications. To address this, researchers have sought models to establish transmission factors for metamaterials, balancing simplifications with precision in vibroacoustic response description. Notably, efforts have been made to describe coupling loss factors in metamaterials, yet challenges persist in addressing acoustic volume interaction. This work aims to present a method for calculating coupling loss factors in acoustic insulation systems based on metamaterials within double-wall arrays, using a Potential-Dissipative Transmission Model (PDTM) with concentrated parameters. The study concludes that integrating the PDTM with SEA achieves a remarkable level of numerical precision in analyzing membrane-type metamaterials within double-wall configurations, particularly at operational frequencies exceeding membrane resonance. While acknowledging potential alternatives, such as hybridizing the TMM with impedance characterization, the PDTM shows promising initial approximations. Further exploration is warranted, particularly in refining methodologies for industrial applications, emphasizing the scalability and robustness of PDTM-based models. Notably, the PDTM demonstrates remarkable sensitivity in estimating metamaterial resonance frequencies, although efficacy may reduce near cavity resonance perturbations. Careful consideration of analytical methodology selection, especially concerning critical frequency points, is advised.